Analysis_Zeisel2015
Package loading
Before performing the analysis, several R-based packages should be installed on your local machine. Note that the packages may require an additional installation of other dependencies. Make sure that you have installed recommended version of the packages and your machine meets the mimimal system requirements for carrying out this analysis.
library(scater)
library(M3Drop)
library(monocle)
library(Seurat)
library(mclust)
library(scran)
library(SC3)Data information
Zeisel2015 is a UMI-based scRNAseq dataset published in Zeisel et al. (2015) (Link to study: http://science.sciencemag.org/content/347/6226/1138) that contains the expression matrix of endogenous, spike-in and mitochondrial genes from 3005 cells from mouse cortex and hippocampus tissues. Additional metadata information are available, including cells origin, type or tissue. For the purpose of this tutorial we stored Zeisel2015 count matrix with metadata information in two separate txt files. We can read these files and create an easy-to-work SingleCellExperiment experiment object.
all.counts <- read.table(file ="data/all.counts.txt")
metadata <- read.table(file ="data/metadata.txt")
sce <- SingleCellExperiment(list(counts=as.matrix(all.counts)), colData=metadata)
sce## class: SingleCellExperiment
## dim: 19896 3005
## metadata(0):
## assays(1): counts
## rownames(19896): Tspan12 Tshz1 ... ERCC-00170 ERCC-00171
## rowData names(0):
## colnames(3005): V3 V4 ... V3006 V3007
## colData names(10): tissue group.. ... level1class level2class
## reducedDimNames(0):
## spikeNames(0):We can explore the information about cells and genes stored in SingleCellExperiment experiment object under colData and rawData slots, respectively.
counts(sce)[1:4,1:4]## V3 V4 V5 V6
## Tspan12 0 0 0 3
## Tshz1 3 1 0 2
## Fnbp1l 3 1 6 4
## Adamts15 0 0 0 0names(colData(sce)) #available metadata information## [1] "tissue" "group.." "total.mRNA.mol" "well"
## [5] "sex" "age" "diameter" "cell_id"
## [9] "level1class" "level2class"table(colData(sce)$tissue) #tissue annotation##
## ca1hippocampus sscortex
## 1314 1691table(colData(sce)$level1class) #cell type annotation##
## astrocytes_ependymal endothelial-mural interneurons
## 224 235 290
## microglia oligodendrocytes pyramidal CA1
## 98 820 939
## pyramidal SS
## 399names(rowData(sce))## character(0)As mentioned, Zeisel2015 dataset contains also the expression of spike-ins and mitochondrial genes. Spike-in gene names usually starts from “ERCC” and mitochondrial genes contain “mt” string.
is.spike <- grepl("^ERCC", rownames(sce))
summary(is.spike)## Mode FALSE TRUE
## logical 19839 57is.mito <- grepl("^mt-", rownames(sce))
summary(is.mito)## Mode FALSE TRUE
## logical 19862 34Quality control and data preprocessing
We can use scater package to automatically calculate several quality metrics per cell and per gene. These metrics will be useful to i.e. detect low quality cells or lowly expressed genes that should be removed from further analysis.
sce <- calculateQCMetrics(sce, feature_controls=list(Spike=is.spike, Mt=is.mito))
colnames(colData(sce))## [1] "tissue"
## [2] "group.."
## [3] "total.mRNA.mol"
## [4] "well"
## [5] "sex"
## [6] "age"
## [7] "diameter"
## [8] "cell_id"
## [9] "level1class"
## [10] "level2class"
## [11] "is_cell_control"
## [12] "total_features_by_counts"
## [13] "log10_total_features_by_counts"
## [14] "total_counts"
## [15] "log10_total_counts"
## [16] "pct_counts_in_top_50_features"
## [17] "pct_counts_in_top_100_features"
## [18] "pct_counts_in_top_200_features"
## [19] "pct_counts_in_top_500_features"
## [20] "total_features_by_counts_endogenous"
## [21] "log10_total_features_by_counts_endogenous"
## [22] "total_counts_endogenous"
## [23] "log10_total_counts_endogenous"
## [24] "pct_counts_endogenous"
## [25] "pct_counts_in_top_50_features_endogenous"
## [26] "pct_counts_in_top_100_features_endogenous"
## [27] "pct_counts_in_top_200_features_endogenous"
## [28] "pct_counts_in_top_500_features_endogenous"
## [29] "total_features_by_counts_feature_control"
## [30] "log10_total_features_by_counts_feature_control"
## [31] "total_counts_feature_control"
## [32] "log10_total_counts_feature_control"
## [33] "pct_counts_feature_control"
## [34] "pct_counts_in_top_50_features_feature_control"
## [35] "pct_counts_in_top_100_features_feature_control"
## [36] "pct_counts_in_top_200_features_feature_control"
## [37] "pct_counts_in_top_500_features_feature_control"
## [38] "total_features_by_counts_Spike"
## [39] "log10_total_features_by_counts_Spike"
## [40] "total_counts_Spike"
## [41] "log10_total_counts_Spike"
## [42] "pct_counts_Spike"
## [43] "pct_counts_in_top_50_features_Spike"
## [44] "pct_counts_in_top_100_features_Spike"
## [45] "pct_counts_in_top_200_features_Spike"
## [46] "pct_counts_in_top_500_features_Spike"
## [47] "total_features_by_counts_Mt"
## [48] "log10_total_features_by_counts_Mt"
## [49] "total_counts_Mt"
## [50] "log10_total_counts_Mt"
## [51] "pct_counts_Mt"
## [52] "pct_counts_in_top_50_features_Mt"
## [53] "pct_counts_in_top_100_features_Mt"
## [54] "pct_counts_in_top_200_features_Mt"
## [55] "pct_counts_in_top_500_features_Mt"Quality metrics per cell
colData(sce)$total_counts[1:5] #Total count for each cell## [1] 29060 29304 38929 40557 27625colData(sce)$total_features_by_counts[1:5] #Number of genes with non zero counts per cell## [1] 4898 4750 6090 5887 4753colData(sce)$pct_counts_Spike[1:5] #Percentage of spike-in counts per cell## [1] 23.07639 21.95946 16.27322 17.33856 21.46968Quality metrics per gene
rowData(sce)$mean_counts[1:5] #Average count per gene## [1] 0.27886855 0.42362729 1.04292845 0.04459235 0.37936772rowData(sce)$n_cells_by_counts[1:5] #Number of cells with non zero counts per gene## [1] 472 573 1167 77 669rowData(sce)$pct_dropout_by_counts[1:5] #Percentage of dropouts per gene## [1] 84.29285 80.93178 61.16473 97.43760 77.73710Plot histograms based on quality metrics
One can plot histograms based on quality metrics to determine possible thresholds for cell/gene filterings.
hist(sce$total_counts, breaks=50, xlab="Library size", ylab="Number of cells")
hist(sce$total_features_by_counts, xlab="Number of expressed genes", breaks=50, ylab="Number of cells")
hist(sce$pct_counts_Spike, xlab="ERCC proportion (%)", ylab="Number of cells", breaks=50)
Automaticly filter outlier cells based on quality metrics
Alternatively, isOutlier function provides an automatic detection of low quality cells based on quality metrics. In this example, we are filtering cells based on library size, number of expressed genes per cell and total count over all spike-in transcripts in each cell. Excluded cells are those with the total number of expressed genes and the total sum of counts more than 3 median absolute deviations below the median across the genes.
libsize.drop <- isOutlier(sce$total_counts, nmads=3, type="lower", log=TRUE)
feature.drop <- isOutlier(sce$total_features_by_counts, nmads=3, type="lower", log=TRUE)
spike.drop <- isOutlier(sce$pct_counts_Spike, nmads=3, type="higher")
sce <- sce[,!(libsize.drop | feature.drop | spike.drop)]
data.frame(ByLibSize=sum(libsize.drop), ByFeature=sum(feature.drop), BySpike=sum(spike.drop), Remaining=ncol(sce))## ByLibSize ByFeature BySpike Remaining
## 1 8 3 8 2989Filter spike-in genes
After quality control on cells, we can remove the expression of spike-in genes from the count matrix.
sce=sce[-which(grepl("^ERCC-", rownames(sce))),]
sce## class: SingleCellExperiment
## dim: 19839 2989
## metadata(0):
## assays(1): counts
## rownames(19839): Tspan12 Tshz1 ... mt-Rnr1 mt-Nd4l
## rowData names(9): is_feature_control is_feature_control_Spike ...
## total_counts log10_total_counts
## colnames(2989): V3 V4 ... V3006 V3007
## colData names(55): tissue group.. ...
## pct_counts_in_top_200_features_Mt
## pct_counts_in_top_500_features_Mt
## reducedDimNames(0):
## spikeNames(0):Filter lowly expressed genes based on the average count per gene
Now, we should filter out lowly expressed genes as they do not provide any insights into the underlying biology. In the filtering we removed lowly expressed genes that are genes with average expression count (adjusted by library size) equal to 0.
rowData(sce)$ave.counts <- calcAverage(sce, exprs_values = "counts", use_size_factors=FALSE)
to.keep <- rowData(sce)$ave.counts > 0
sce <- sce[to.keep,]
summary(to.keep)## Mode FALSE TRUE
## logical 2 19837dim(sce)## [1] 19837 2989Explore highly expressed genes, if required filter overexpressed features
We can also explore highly and overexpressed genes. The overexpressed genes, are those genes which expression is higher than others by several magnitudes. Overexpressed genes can bias further procedures such as clustering, therefore, they should be removed before performing downstream analysis. Note that one of the most common overexpressed gene is “Malat1”.
plotHighestExprs(sce, exprs_values = "counts")
sce <- sce[-which(rownames(sce)=="Malat1"),]
dim(sce)## [1] 19836 2989Perform standard normalization by computing counts per million (CPM)
After quality control and filtering, one should normalize the dataset to remove potential technical bias. One strategy is to use CPM (Count Per Million) normalization which is a correction to remove the noise related to sequencing depth. CPM divides each count by its total sum (across all the genes) and multiplies by one million. In this way, each cell has the same total sum of the counts.
cpm(sce) <- calculateCPM(sce, use_size_factors=FALSE)
cpm(sce)[1:4,1:4]## V3 V4 V5 V6
## Tspan12 0.0000 0.00000 0.0000 92.95696
## Tshz1 139.3275 45.45455 0.0000 61.97131
## Fnbp1l 139.3275 45.45455 191.3448 123.94261
## Adamts15 0.0000 0.00000 0.0000 0.00000Perform normalization using decnvolution method
Another strategy, more suitable for scRNAseq data, is deconvolution method implemented in scran package. The deconvolution method normalizes data by cells-pooled size factors that account for dropout biases. More details about this normalization technique can be found in study https://genomebiology.biomedcentral.com/articles/10.1186/s13059-016-0947-7.
set.seed(100)
clusters <- quickCluster(sce, min.size=200, min.mean=0.1, method="igraph")
sce <- computeSumFactors(sce, cluster=clusters, min.mean=0.1)
sce <- scater::normalize(sce, return_log = FALSE)
normcounts(sce)[1:4,1:4]## V3 V4 V5 V6
## Tspan12 0.000000 0.0000000 0.000000 1.2865579
## Tshz1 1.896026 0.6416602 0.000000 0.8577053
## Fnbp1l 1.896026 0.6416602 2.532498 1.7154106
## Adamts15 0.000000 0.0000000 0.000000 0.0000000Perform feature selection to retrieve most variable genes
Feature selection step is aimed at preserving biologically relevant information in the dataset and improving computational efficiency of downstream analyses. In most of the cases, it seeks for highly variable genes based on mean/variance relationship. M3Drop is one of the packages for automatic detection of most variable genes. It first calculates the mean and square coefficient of variation and fits the quadratic curve between the two variables. Then a chi-square test is used to find high variable genes which are significantly above the curve.
hvg_genes <- BrenneckeGetVariableGenes(normcounts(sce), fdr = 0.01, minBiolDisp = 0.5)
length(hvg_genes)## [1] 14225scran package also allows to identify genes that drive biological heterogeneity by modelling per-gene variance. The method first decomposes the total variance of each gene into its biological and technical components then fits mean-variance trend to the normalized log-expression values. By default, the method uses spike-in genes to identify technical noise. If no spike-ins are available, the method will use all the features with assumption that technical noise is the major contributor to the variance of most genes in the dataset. Once technical component is estimated it will be substracted from the total variance to obtain the biological component for each gene. Genes with high biological components are of interest. Note that the method requires to input log-transformed normalized counts and outputs an ordered list of all genes from which the user has to extract a certain number of top features for use in downstream analysis.
assay(sce, "logcounts") <- log2(normcounts(sce)+1)
fit <- trendVar(sce, parametric=TRUE, use.spikes=FALSE)
decomp <- decomposeVar(sce, fit)
head(decomp)## DataFrame with 6 rows and 6 columns
## mean total bio
## <numeric> <numeric> <numeric>
## Tspan12 0.21954217578161 0.367997453453532 0.0676731873287152
## Tshz1 0.311930968051195 0.549001316751025 0.138350625999446
## Fnbp1l 0.61796543640819 0.839797618303715 0.0845728838805125
## Adamts15 0.035777983570672 0.0699552575563804 0.0165716888849863
## Cldn12 0.279720893210915 0.383207030299019 0.010109269426282
## Rxfp1 0.0365498687107355 0.0473109676070912 -0.00722212286053495
## tech p.value FDR
## <numeric> <numeric> <numeric>
## Tspan12 0.300324266124817 2.00236966401108e-16 1.16889360374702e-15
## Tshz1 0.410650690751579 1.90913067042286e-32 1.58915299951775e-31
## Fnbp1l 0.755224734423203 1.42457379368776e-05 5.61786198242353e-05
## Adamts15 0.0533835686713941 3.28461490021999e-28 2.5107368462722e-27
## Cldn12 0.373097760872737 0.147643066563371 0.420420308405258
## Rxfp1 0.0545330904676262 0.999999957325667 1genes_ordered <- order(decomp$bio, decreasing=TRUE)
hvg_genes <- genes_ordered[1:500]
length(hvg_genes)## [1] 500Data visualization
For reducing dimension of the data you can use PCA, tSNE or UMAP techniques implemented in scater package. Note that projections should be applied to normalized and log-transformed count matrices. For reproducibility of tSNE and UMAP projections - set the seed for generating random variables.
plotPCA(sce, colour_by="level1class", run_args=c(exprs_values = "logcounts")) ## Warning: 'add_ticks' is deprecated.
## Use '+ geom_rug(...)' instead.
set.seed(100)
plotTSNE(sce, colour_by="level1class", run_args=c(exprs_values = "logcounts"))## Warning: 'add_ticks' is deprecated.
## Use '+ geom_rug(...)' instead.
plotUMAP(sce, colour_by="level1class", run_args=c(exprs_values = "logcounts"))## Warning: 'add_ticks' is deprecated.
## Use '+ geom_rug(...)' instead.
Exercise
How the projections would change if you would plot raw or CPM counts followed by log-transformation?
Additional plots
You can use colour_by argument to color points in any of the above projections by a selected marker gene or any information stored in the annotation. Additional violin plots allow you to i.e. visualize the expression of the selected gene across all the cells from a given cell type. For the illustrative purpose, we used Gad1 gene taken from the literature, which is a marker for interneuron cell type in the cortex tissue.
set.seed(100)
plotTSNE(sce, colour_by="Gad1", run_args=c(exprs_values = "logcounts")) #marker for interneurons## Warning: 'add_ticks' is deprecated.
## Use '+ geom_rug(...)' instead.
plotExpression(sce, "Gad1", x = "level1class", colour_by = "level1class", exprs_values = "logcounts") 
Clustering
To cluster cells we can use SC3 package. SC3 is a consensus clustering method for single-cell RNA-seq data. It first calculates distances between the cells using three metrics: Euclidean, Pearson, and Spearman. On each of the obtained distance matrix two transformations are applied: PCA and Laplacian graph. Then K-Means clustering technique is used to cluster the transformed distance matrices subject to the first d eigenvectors. In result, several individual clusterings are obtained which are further combined into a single consensus clustering using Cluster-based Similarity Partitioning Algorithm (CSPA). Note that when using SC3, one can first estimate the number of populations to be used in the clustering.
sce <- sc3_estimate_k(sce)## Estimating k...k_input <- metadata(sce)$sc3$k_estimation
k_input #number of estimated clusters## [1] 32rowData(sce)$feature_symbol <- rownames(sce)
sce <- sc3(sce, ks = k_input, gene_filter = FALSE, biology = TRUE)## Setting SC3 parameters...## Your dataset contains more than 2000 cells. Adjusting the nstart parameter of kmeans to 50 for faster performance...## Calculating distances between the cells...## Performing transformations and calculating eigenvectors...## Performing k-means clustering...## Calculating consensus matrix...## Calculating biology...table(colData(sce)[paste0("sc3_",k_input, "_clusters")][[1]])##
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## 335 66 286 11 2 26 13 92 86 30 6 80 92 103 6 10 9 182
## 19 20 21 22 23 24 25 26 27 28 29 30 31 32
## 9 71 80 226 41 64 56 135 4 111 304 32 43 378Evaluate clustering output based on annotation
If the cell annotation is available, one can measure the effectiveness of clustering output using Adjusted Rand Index (ARI). ARI index measures similarity between the partition obtained from clustering and the partition obtained from dataset annotation. The values of the ARI range can be negative if the agreement of the partitions is worse then the agreement expected by chance, or between 0 and 1 for clustering better then chance. ARI close to 1 indicate high accuracy of the method in detecting annotated cell populations.
adjustedRandIndex(colData(sce)[paste0("sc3_",k_input, "_clusters")][[1]],sce$level1class)## [1] 0.3580484Exercise
How the clustering would change if you would use true number of cell populations (taken from annotation) in the inference of SC3?
Complete data analysis using Monocle package
Create CellDataSet data object
CellDataSet data object is similar for SingleCellExperiment object. It stores information about the experiment (i.e. expression matrix and metadata) in “slots”. Note that when creating a new CellDataSet data should not be normalized - Monocle, when performing downstream analysis steps, normalizes the data internally.
rowData(sce)$gene_short_name <- rownames(sce)
pd <- new("AnnotatedDataFrame", data = data.frame(colData(sce))) #cell info
fd <- new("AnnotatedDataFrame", data = data.frame(rowData(sce))) #gene info
cds <- newCellDataSet(cellData = counts(sce), phenoData = pd, featureData = fd, expressionFamily=VGAM::negbinomial.size())
cds## CellDataSet (storageMode: environment)
## assayData: 19836 features, 2989 samples
## element names: exprs
## protocolData: none
## phenoData
## sampleNames: V3 V4 ... V3007 (2989 total)
## varLabels: tissue group.. ... Size_Factor (58 total)
## varMetadata: labelDescription
## featureData
## featureNames: Tspan12 Tshz1 ... mt-Nd4l (19836 total)
## fvarLabels: is_feature_control is_feature_control_Spike ...
## gene_short_name (17 total)
## fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
## Annotation:Extract highly variable genes for further analysis
cds <- BiocGenerics::estimateSizeFactors(cds)
cds <- estimateDispersions(cds)## Removing 132 outliersdisp <- dispersionTable(cds)
head(disp)## gene_id mean_expression dispersion_fit dispersion_empirical
## 1 Tspan12 0.27371308 5.352092 9.664429
## 2 Tshz1 0.41233507 3.788779 8.705790
## 3 Fnbp1l 0.83029734 2.234915 2.957010
## 4 Adamts15 0.04653374 28.054145 71.442708
## 5 Cldn12 0.30721173 4.845039 5.144358
## 6 Rxfp1 0.03723447 34.885324 14.381728hvg <- subset(disp, mean_expression >= 0.5 & dispersion_empirical >= 0.1)
cds <- setOrderingFilter(cds, ordering_genes = hvg$gene_id)
plot_ordering_genes(cds)## Warning: Transformation introduced infinite values in continuous y-axis
cds <- cds[hvg$gene_id,]Reduce dimension of the data and cluster cells to detect cell populations
cds <- reduceDimension(cds, max_components = 2, reduction_method = 'tSNE', verbose = T)## Warning in if (method == "PCA") {: the condition has length > 1 and only
## the first element will be usedcds <- clusterCells(cds, num_clusters = NULL)## Distance cutoff calculated to 3.325859Compare clusterization with annotated cell types
p1 <- monocle::plot_cell_clusters(cds, color_by = 'Cluster')
p1
p2 <- monocle::plot_cell_clusters(cds, color_by = 'level1class')
p2
Compute Adjusted Rand Index
adjustedRandIndex(cds$Cluster,cds$level1class)## [1] 0.7575202Complete data analysis using Seurat package
Create Seurat object
seur <- CreateSeuratObject(raw.data = counts(sce), meta.data = data.frame(colData(sce)), min.cells = 0, min.genes = 0)
seur## An object of class seurat in project SeuratProject
## 19836 genes across 2989 samples.Seurat require to log-normalize and scale data before performing clustering
seur <- NormalizeData(seur, normalization.method = "LogNormalize")
seur@data[1:4,1:4]## 4 x 4 sparse Matrix of class "dgCMatrix"
## V3 V4 V5 V6
## Tspan12 . . . 0.6572970
## Tshz1 0.8726628 0.3746934 . 0.4822490
## Fnbp1l 0.8726628 0.3746934 1.069337 0.8062196
## Adamts15 . . . .Extract highly variable genes for further analysis
seur <- FindVariableGenes(object = seur)
Scale the data
seur<- Seurat::ScaleData(object = seur)## Scaling data matrixReduce dataset dimension with PCA and clusterize cells
seur <- RunPCA(object = seur, pc.genes=seur@var.genes)
seur <- FindClusters(object = seur, reduction.type="pca")table(seur@ident)##
## 0 1 2 3 4 5 6
## 848 841 366 318 276 257 83Compare clusterization with annotated cell types
Seurat::DimPlot(seur, group.by = "ident", reduction.use = "pca")
Seurat::DimPlot(seur, group.by = "level1class", reduction.use = "pca")
Compute Adjusted Rand Index
adjustedRandIndex(as.numeric(seur@ident), seur@meta.data$level1class)## [1] 0.8072137Package versions used in this analysis
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.3 LTS
##
## Matrix products: default
## BLAS: /usr/lib/atlas-base/atlas/libblas.so.3.0
## LAPACK: /usr/lib/atlas-base/atlas/liblapack.so.3.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] parallel stats4 stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] SC3_1.10.1 scran_1.10.2
## [3] mclust_5.4.3 Seurat_2.3.4
## [5] cowplot_0.9.4 monocle_2.99.2
## [7] L1Graph_0.1.1 lpSolveAPI_5.5.2.0-17
## [9] DDRTree_0.1.5 irlba_2.3.3
## [11] igraph_1.2.4 Matrix_1.2-17
## [13] M3Drop_1.8.1 numDeriv_2016.8-1
## [15] scater_1.10.1 ggplot2_3.1.0
## [17] SingleCellExperiment_1.4.1 SummarizedExperiment_1.12.0
## [19] DelayedArray_0.8.0 BiocParallel_1.16.6
## [21] matrixStats_0.54.0 Biobase_2.42.0
## [23] GenomicRanges_1.34.0 GenomeInfoDb_1.18.2
## [25] IRanges_2.16.0 S4Vectors_0.20.1
## [27] BiocGenerics_0.28.0
##
## loaded via a namespace (and not attached):
## [1] prabclus_2.2-7 R.methodsS3_1.7.1
## [3] coda_0.19-2 pkgmaker_0.27
## [5] tidyr_0.8.3 acepack_1.4.1
## [7] bit64_0.9-7 knitr_1.22
## [9] R.utils_2.8.0 data.table_1.12.0
## [11] rpart_4.1-13 RCurl_1.95-4.12
## [13] doParallel_1.0.14 metap_1.1
## [15] snow_0.4-3 RANN_2.6.1
## [17] VGAM_1.1-1 combinat_0.0-8
## [19] proxy_0.4-23 future_1.12.0
## [21] bit_1.1-14 webshot_0.5.1
## [23] httpuv_1.5.0 assertthat_0.2.1
## [25] viridis_0.5.1 xfun_0.5
## [27] evaluate_0.13 promises_1.0.1
## [29] DEoptimR_1.0-8 caTools_1.17.1.2
## [31] DBI_1.0.0 htmlwidgets_1.3
## [33] sparsesvd_0.1-4 spdep_1.0-2
## [35] purrr_0.3.2 RSpectra_0.13-1
## [37] crosstalk_1.0.0 dplyr_0.8.0.1
## [39] backports_1.1.3 trimcluster_0.1-2.1
## [41] gbRd_0.4-11 deldir_0.1-16
## [43] Cairo_1.5-10 ROCR_1.0-7
## [45] withr_2.1.2 robustbase_0.93-4
## [47] checkmate_1.9.1 cluster_2.0.7-1
## [49] ape_5.3 segmented_0.5-3.0
## [51] lazyeval_0.2.2 crayon_1.3.4
## [53] hdf5r_1.1.1 labeling_0.3
## [55] glmnet_2.0-16 edgeR_3.24.3
## [57] pkgconfig_2.0.2 slam_0.1-45
## [59] units_0.6-2 nlme_3.1-137
## [61] vipor_0.4.5 nnet_7.3-12
## [63] rlang_0.4.0 globals_0.12.4
## [65] diptest_0.75-7 miniUI_0.1.1.1
## [67] registry_0.5-1 doSNOW_1.0.16
## [69] ggrastr_0.1.7 lmtest_0.9-36
## [71] rngtools_1.3.1 Rhdf5lib_1.4.3
## [73] boot_1.3-20 zoo_1.8-5
## [75] base64enc_0.1-3 beeswarm_0.2.3
## [77] ggridges_0.5.1 pheatmap_1.0.12
## [79] png_0.1-7 viridisLite_0.3.0
## [81] bitops_1.0-6 R.oo_1.22.0
## [83] KernSmooth_2.23-15 DelayedMatrixStats_1.4.0
## [85] rgl_0.100.19 doRNG_1.7.1
## [87] classInt_0.3-1 lars_1.2
## [89] stringr_1.4.0 manipulateWidget_0.10.0
## [91] scales_1.0.0 magrittr_1.5
## [93] plyr_1.8.4 ica_1.0-2
## [95] gplots_3.0.1.1 bibtex_0.4.2
## [97] gdata_2.18.0 zlibbioc_1.28.0
## [99] compiler_3.5.1 HSMMSingleCell_1.2.0
## [101] lsei_1.2-0 bbmle_1.0.20
## [103] RColorBrewer_1.1-2 rrcov_1.4-7
## [105] fitdistrplus_1.0-14 dtw_1.20-1
## [107] XVector_0.22.0 LearnBayes_2.15.1
## [109] listenv_0.7.0 pbapply_1.4-0
## [111] htmlTable_1.13.1 Formula_1.2-3
## [113] MASS_7.3-51.3 tidyselect_0.2.5
## [115] stringi_1.4.3 densityClust_0.3
## [117] yaml_2.2.0 locfit_1.5-9.1
## [119] latticeExtra_0.6-28 ggrepel_0.8.0
## [121] pbmcapply_1.3.1 grid_3.5.1
## [123] tools_3.5.1 rstudioapi_0.10
## [125] foreach_1.4.4 foreign_0.8-71
## [127] gridExtra_2.3 Rtsne_0.15
## [129] digest_0.6.18 FNN_1.1.3
## [131] shiny_1.2.0 qlcMatrix_0.9.7
## [133] fpc_2.1-11.1 Rcpp_1.0.1
## [135] SDMTools_1.1-221 later_0.8.0
## [137] WriteXLS_4.1.0 httr_1.4.0
## [139] sf_0.7-3 npsurv_0.4-0
## [141] kernlab_0.9-27 Rdpack_0.10-1
## [143] colorspace_1.4-1 reticulate_1.11.1
## [145] umap_0.2.0.0 splines_3.5.1
## [147] statmod_1.4.30 expm_0.999-4
## [149] sp_1.3-1 flexmix_2.3-15
## [151] plotly_4.8.0 spData_0.3.0
## [153] xtable_1.8-3 jsonlite_1.6
## [155] dynamicTreeCut_1.63-1 modeltools_0.2-22
## [157] R6_2.4.0 gmodels_2.18.1
## [159] Hmisc_4.2-0 pillar_1.4.2
## [161] htmltools_0.3.6 mime_0.6
## [163] glue_1.3.1 BiocNeighbors_1.0.0
## [165] class_7.3-15 codetools_0.2-16
## [167] pcaPP_1.9-73 tsne_0.1-3
## [169] mvtnorm_1.0-10 lattice_0.20-38
## [171] tibble_2.1.1 mixtools_1.1.0
## [173] ggbeeswarm_0.6.0 gtools_3.8.1
## [175] survival_2.44-1.1 limma_3.38.3
## [177] rmarkdown_1.12 docopt_0.6.1
## [179] fastICA_1.2-1 munsell_0.5.0
## [181] e1071_1.7-1 rhdf5_2.26.2
## [183] GenomeInfoDbData_1.2.0 iterators_1.0.10
## [185] HDF5Array_1.10.1 reshape2_1.4.3
## [187] gtable_0.3.0